3 ms·

> I began to realise that Jean had a certain collection of tools, heuristics, and principles that he regarded as “basic”, such as dyadic decomposition and the u

> I began to realise that Jean had a certain collection of tools, heuristics, and principles that he regarded as “basic”, such as dyadic decomposition and the uncertainty principle, and by working “modulo” these tools (that is, by regarding any step consisting solely of application of these tools as trivial), one could proceed much more rapidly and efficiently. Does anybody know what those "basic" tools and heuristics are? Has anybody created a list of them somewhere for others to understand the papers more easily?

southerndrift 8y ago
The answer is in the blog comments: >Dear Terry, >Have you ever considered writing a blog post on “Bourgain’s toolbox” summarizing the kinds of techniques used continually (without explanation) in his papers? >[...] Tao's final conclusion, besides other hints like http://www.tricki.org/ http://www.tricki.org/ is: > I think that ultimately the best way to acquire these tools is to constantly be exposed to interesting new mathematics, whether it is through reading a challenging paper from an expert, or listening to a talk on a topic outside your own specialty, or by working (particularly with collaborators) on a problem outside of your own comfort zone. Bourgain is not the only author whose writings happen to be particularly worth investing the effort to properly read; I for instance found reading Szemeredi’s work or Perelman’s work to be a broadly similar experience, and I am sure that there are several other mathematicians with this property also.
- southerndrift 8y ago
  Though: >Eventually, though, and with the help of Eli Stein and Tom Wolff, I managed to decode the steps which had mystified me – and my impression of the paper reversed completely. If he hasn't managed to do this on his own, how should anybody else acquire those tools just by reading challenging papers?

southerndrift 8y ago

The answer is in the blog comments: >Dear Terry, >Have you ever considered writing a blog post on “Bourgain’s toolbox” summarizing the kinds of techniques used continually (without explanation) in his papers? >[...] Tao's final conclusion, besides other hints like http://www.tricki.org/ http://www.tricki.org/ is: > I think that ultimately the best way to acquire these tools is to constantly be exposed to interesting new mathematics, whether it is through reading a challenging paper from an expert, or listening to a talk on a topic outside your own specialty, or by working (particularly with collaborators) on a problem outside of your own comfort zone. Bourgain is not the only author whose writings happen to be particularly worth investing the effort to properly read; I for instance found reading Szemeredi’s work or Perelman’s work to be a broadly similar experience, and I am sure that there are several other mathematicians with this property also.

southerndrift 8y ago
Though: >Eventually, though, and with the help of Eli Stein and Tom Wolff, I managed to decode the steps which had mystified me – and my impression of the paper reversed completely. If he hasn't managed to do this on his own, how should anybody else acquire those tools just by reading challenging papers?